Your shoes always matter.
"Walking Shoes" and Trail Walking Shoes are neither running shoes nor hiking shoes, generally speaking. Like many European cities, New York City is a walking town. New Yorkers walk a lot. In fact, in many circumstances in Manhattan you can get to your destination as fast, or faster, than you can with a cab or an Uber.
For urban walking and urban hiking, you want walking shoes. They are more like heavy-duty sneakers.
I suppose you want to use the lightest weight shoe for your purpose. No bouldering boots for exploring Vienna: Trail Walking Shoe vs. Hiking Shoe. We like Merrells and Keens for either long-distance urban or trail walking.
The top ten walking shoes reviewed
Things to consider when buying walking shoes
Also, on another topic, sales on serious hiking shoes at Sierra Trading Post